Ipomea covers a lot of ground in the Convolvulaceae family! It also includes the Sweet potato which sometimes lends its characteristic leaf to its cousin morning glory. I wouldn’t trouble with transplanting. Let it reseed.

Don’t walk, RUN as fast as you can from this innocent looking plant. It is your most invasive nightmare come true! It’s name is Field Bindweed and it showed up as an “extra” with a lilac I bought 30 years ago. It very quickly took over my yard. After several years of fighting it I tried to dig it up. The surface roots looked like a mass of spaghetti and the deeper ones were huge. The roots 3 feet deep (!!!) were very tough and as large as my pinky finger. Worst of all they had morphed into a mutant root which had a completely woody outside which protected a healthy vigorous inside. The ability to grow so deep coupled with a tough woody shield makes it impossible to kill with spray. The leaves and delicate stems are simply not strong enough to carry enough poison to the giant woody roots. Any tiny piece can repopulate your yard AND IT CAN LIE DORMANT FOR YEARS AND THEN COME BACK! I went to the nursery where I got it (since closed) and it had invaded a huge number of their plants. The Field Bindweed was so invasive that the nursery was unable to control it and keep it out of their pots. Fellow garners ask me how I finally got rid of it: I moved.